timo-pierre-schrader/asp-solver-in-the-loop-preference-dataset

A Solver-in-the-Loop Framework for Improving LLMs on Answer Set Programming for Logic Puzzle Solving - Experiment Resources 🤖 🔄 ⚙️

This repository contains the dataset for the following publication:

Timo Pierre Schrader, Lukas Lange, Tobias Kaminski, Simon Razniewski, Annemarie Friedrich. A Solver-in-the-Loop Framework for Improving LLMs on Answer Set Programming for Logic Puzzle Solving AAAI 2026.

For the code, please refer to GitHub.

Please cite this paper if using the dataset or the code.

Methodological Overview 💡

In our paper, we propose a novel solver-in-the-loop method for automatically generating silver standard training data for answer set programming (ASP) code. For that, we first start by processing a combinatorial problem, formulated in natural language, using an LLM by prompting it to create $n$ alternative ASP encodings. We do this once for every single problem description, choice rule, and constraints/rules. Now, for the set of $n$ alternatives, we obtain feedback from the external ASP solver, in our case clingo based on whether a partial ASP encoding produces errors, is unsatisfiable, or produdes the actual correct answer. We can then categorize each generated statement into either chosen or rejected. Furthermore, since ASP is declarative, we can combine partial encodings into longer ones, thereby obtaining more diverse training data.

Models trained on this silver standard training data exhibit superior performance on the test split of LogicPuzzles as well as the harder GridPuzzles dataset with only minimal prompt engineering effort necessary.

Test-Time Additions ➕

We propose to also use the solver-in-the-loop setup during inference. For that, we introduce a problem-specific reward function $f_{reward}$ that aims at judging how "promising" a generated alternative is. In our problem setting, we decide to prefer partial encodings that produce as few answers as possible as we want to arrive at a single answer in the end when having generated the complete ASP encoding for the problem, i.e., problem descriptions, choice rule, and all constraints/rules were processed.

Using this reward function, we obtain a search tree during inference, which we can also use for backtracking if all alternatives were judged negatively according to $f_{reward}$, even after re-generating another $2 \cdot n$ alternatives.

We encourage the interested reader to introduce novel reward functions for other types of problems that can be solved using ASP. 😊

Data Source

Our dataset is based on the following publicly available dataset:

• gpt-asp-rules: 4d3357830175cbf4d70baccf2ff5a9587d74b519

We deeply thank the authors for providing this dataset and highly encourage to read the related publications:

• Leveraging Large Language Models to Generate Answer Set Programs, Adam Ishay, Zhun Yang, and Joohyung Lee. 2023. In Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning (KR '23), Vol. 20. Article 37, 374–383. https://doi.org/10.24963/kr.2023/37Arindam Mitra and Chitta Baral. 2015. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1023–1033, Lisbon, Portugal. Association for Computational Linguistics.

Data Generation Info 🗂️

We used the following two models for automatically obtaining ASP training data:

• meta-llama/Llama-3.3-70B-Instruct (snapshot: 6f6073b423013f6a7d4d9f39144961bfbfbc386b)
• Qwen/Qwen3-32B (snapshot: 9216db5781bf21249d130ec9da846c4624c16137)

License

The ASP preference dataset is released under the CC BY-SA 4.0 license. See the LICENSE file for details.

Citation

If you use our software or dataset in your scientific work, please cite our paper:

@article{Schrader_Lange_Kaminski_Razniewski_Friedrich_2026, title={A Solver-in-the-Loop Framework for Improving LLMs on Answer Set Programming for Logic Puzzle Solving}, volume={40}, url={https://ojs.aaai.org/index.php/AAAI/article/view/39714}, DOI={10.1609/aaai.v40i30.39714}, number={30}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Schrader, Timo Pierre and Lange, Lukas and Kaminski, Tobias and Razniewski, Simon and Friedrich, Annemarie}, year={2026}, month={Mar.}, pages={25226–25234} }